What is the derivative of 3^{sin(x}+(e^{-x})/2) ?

The derivative of 3^{sin(x}+(e^{-x})/2) is ln(3)*3^{sin(x)}cos(x)-1/2 e^{-x}

What is the first derivative of 3^{sin(x}+(e^{-x})/2) ?

The first derivative of 3^{sin(x}+(e^{-x})/2) is ln(3)*3^{sin(x)}cos(x)-1/2 e^{-x}

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\frac{d}{d x} (3^{s i n (x)} + \frac{e ^{- x}}{2})

ln (3) \cdot 3^{s i n (x)} cos (x) - \frac{1}{2} e^{- x}

Solution steps

\frac{d}{d x} (3^{s i n (x)} + \frac{e ^{- x}}{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3^{s i n (x)}) + \frac{d}{d x} (\frac{e ^{- x}}{2})

\frac{d}{d x} (3^{s i n (x)}) = ln (3) \cdot 3^{s i n (x)} cos (x)

\frac{d}{d x} (\frac{e ^{- x}}{2}) = - \frac{1}{2} e^{- x}

= ln (3) \cdot 3^{s i n (x)} cos (x) - \frac{1}{2} e^{- x}

5 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

\frac{d}{d x} (49 - x^{2} - y^{2})

\frac{d}{d x} (c x)

\int \frac{2}{x ^{3} + 3 x ^{2} + 2 x} d x

What is the derivative of 3^{sin(x}+(e^{-x})/2) ?
The derivative of 3^{sin(x}+(e^{-x})/2) is ln(3)*3^{sin(x)}cos(x)-1/2 e^{-x}
What is the first derivative of 3^{sin(x}+(e^{-x})/2) ?
The first derivative of 3^{sin(x}+(e^{-x})/2) is ln(3)*3^{sin(x)}cos(x)-1/2 e^{-x}